Question 1. 3+5=8 marks

b) The equation x2 6x + y2 + 8y = 24 describes a circle.

i `Complete the square` to write the equation in form (x a)2 + (y b)2 = r2

ii Write down the coordinates of the centre of the circle and its radius.

iii What are the coordinates of the uppermost point of the circle?

Question 2. 3+2+4+4=13 marks

Consider the function with piecewise denition

a) Can the denition of f(x) when x 6= 1 be simplied? If yes, what is the simpler expression?

b) Sketch the graph of f(x) carefully for x between -5 and 3.

c) What is the domain of this function? What is its range? Justify your answers.

d) Is f(x) continuous? Assess this property formally.

Question 9. 4+5+2=11 marks

A particle moves along a number line so that its position at time t is given by

s(t) = t3 10t2 + 12t (t 0)

where s is in centimetres and t in seconds.

a) When does the particle change direction ? (i.e. when does its velocity change from nega-

tive to positive or vice versa?)

b) When is the particle moving to the right?

c) What is the furthest left the particle attains?

total 90 marks

4

2018-03-05
Maths